Construction of L2-orthogonal elements of arbitrary order for Local Projection Stabilization

F. Schieweck; P. Skrzypacz; L. Tobiska

doi:10.1016/j.amc.2018.04.070

Construction of L²-orthogonal elements of arbitrary order for Local Projection Stabilization

F. Schieweck, P. Skrzypacz, L. Tobiska

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We construct L²-orthogonal conforming elements of arbitrary order for the Local Projection Stabilization (LPS). L²-orthogonal basis functions lead to a diagonal mass matrix which can be advantageous for time discretizations. We prove that the constructed family of finite elements satisfies a local inf-sup condition. Additionally, we investigate the size of the local inf-sup constant with respect to the polynomial degree. Our numerical tests show that the discrete solution is oscillation-free and of optimal accuracy in the regions away from the boundary or interior layers.

Original language	English
Pages (from-to)	87-101
Number of pages	15
Journal	Applied Mathematics and Computation
Volume	337
DOIs	https://doi.org/10.1016/j.amc.2018.04.070
Publication status	Published - Nov 15 2018

Keywords

L-orthogonal elements
Local projection stabilization

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2018.04.070

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title = "Construction of L2-orthogonal elements of arbitrary order for Local Projection Stabilization",

abstract = "We construct L2-orthogonal conforming elements of arbitrary order for the Local Projection Stabilization (LPS). L2-orthogonal basis functions lead to a diagonal mass matrix which can be advantageous for time discretizations. We prove that the constructed family of finite elements satisfies a local inf-sup condition. Additionally, we investigate the size of the local inf-sup constant with respect to the polynomial degree. Our numerical tests show that the discrete solution is oscillation-free and of optimal accuracy in the regions away from the boundary or interior layers.",

keywords = "L-orthogonal elements, Local projection stabilization",

author = "F. Schieweck and P. Skrzypacz and L. Tobiska",

note = "Funding Information: The presented work in this paper was supported through the research grant 090118FD5347 from the Nazarbayev University. Publisher Copyright: {\textcopyright} 2018 Elsevier Inc. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.",

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AU - Schieweck, F.

AU - Skrzypacz, P.

AU - Tobiska, L.

N1 - Funding Information: The presented work in this paper was supported through the research grant 090118FD5347 from the Nazarbayev University. Publisher Copyright: © 2018 Elsevier Inc. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2018/11/15

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N2 - We construct L2-orthogonal conforming elements of arbitrary order for the Local Projection Stabilization (LPS). L2-orthogonal basis functions lead to a diagonal mass matrix which can be advantageous for time discretizations. We prove that the constructed family of finite elements satisfies a local inf-sup condition. Additionally, we investigate the size of the local inf-sup constant with respect to the polynomial degree. Our numerical tests show that the discrete solution is oscillation-free and of optimal accuracy in the regions away from the boundary or interior layers.

AB - We construct L2-orthogonal conforming elements of arbitrary order for the Local Projection Stabilization (LPS). L2-orthogonal basis functions lead to a diagonal mass matrix which can be advantageous for time discretizations. We prove that the constructed family of finite elements satisfies a local inf-sup condition. Additionally, we investigate the size of the local inf-sup constant with respect to the polynomial degree. Our numerical tests show that the discrete solution is oscillation-free and of optimal accuracy in the regions away from the boundary or interior layers.

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KW - Local projection stabilization

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